A201995 Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.

6, 0, 0, 0, 1, 4, 5, 8, 0, 2, 8, 4, 3, 0, 4, 4, 8, 6, 5, 6, 4, 3, 9, 4, 1, 2, 1, 7, 5, 3, 7, 8, 4, 8, 3, 8, 3, 7, 4, 0, 5, 8, 8, 6, 1, 5, 9, 4, 4, 5, 6, 8, 5, 8, 5, 0, 3, 5, 1, 0, 7, 9, 5, 0, 0, 8, 5, 9, 7, 4, 1, 6, 7, 4, 7, 5, 1, 0, 0, 3, 5, 9, 2, 4, 1, 5, 0, 3, 4, 2, 5, 6, 0

Offset

1,1

Links

Table of n, a(n) for n=1..93.

B. K. Choudhury, The Riemann zeta-function and its derivatives, Proc. R. Soc. Lond A 445 (1995) 477-499.

Formula

zeta'''(2)= -Sum_{k>=1} log^3(k)/k^2.

Equals 3! + Sum_{k>=0} (-1)^k*gamma(3+k)/k!, where gamma(.) are the Stieltjes constants A001620, A082633, A086279 etc. [Choudhury, Thm. 4]

Example

zeta'''(2) = -6.00014580284304486564394121753784..

Maple

evalf(Zeta(3, 2));

Mathematica

RealDigits[ Zeta'''[2], 10, 93] // First (* Jean-François Alcover, Feb 20 2013 *)

Crossrefs

Cf. A013661, A073002, A201994.

Sequence in context: A270606 A087255 A097606 * A226784 A281319 A174431

Adjacent sequences: A201992 A201993 A201994 * A201996 A201997 A201998

Keyword

cons,nonn

Author

R. J. Mathar, Dec 07 2011

Status

approved